Defining parameters
| Level: | \( N \) | \(=\) | \( 162 = 2 \cdot 3^{4} \) |
| Weight: | \( k \) | \(=\) | \( 9 \) |
| Character orbit: | \([\chi]\) | \(=\) | 162.f (of order \(18\) and degree \(6\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 27 \) |
| Character field: | \(\Q(\zeta_{18})\) | ||
| Sturm bound: | \(243\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{9}(162, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 1332 | 144 | 1188 |
| Cusp forms | 1260 | 144 | 1116 |
| Eisenstein series | 72 | 0 | 72 |
Trace form
Decomposition of \(S_{9}^{\mathrm{new}}(162, [\chi])\) into newform subspaces
The newforms in this space have not yet been added to the LMFDB.
Decomposition of \(S_{9}^{\mathrm{old}}(162, [\chi])\) into lower level spaces
\( S_{9}^{\mathrm{old}}(162, [\chi]) \simeq \) \(S_{9}^{\mathrm{new}}(27, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(54, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(81, [\chi])\)\(^{\oplus 2}\)